Multiple choice

Three science classes A, B and C take a Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. Then the average score of classes A, B and C is तीन विज्ञान की कक्षाएँ A, B और C विज्ञान की परीक्षा देती हैं | कक्षा A का औसत स्कोर 83 है | कक्षा B का औसत स्कोर 76 है | कक्षा C का औसत स्कोर 85 है | कक्षा A और B का औसत स्कोर 79 है और कक्षा B और C का औसत स्कोर 81 है | तो कक्षाओं A, B और C का औसत स्कोर है -

  1. 81.5

  2. 81

  3. 80.5

  4. 80
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A Correct answer
Explanation

Let the number of students in classes A, B, C be a, b, c respectively. Given: average of A = 83 (so sum = 83a), average of B = 76 (sum = 76b), average of C = 85 (sum = 85c). Also: average of A and B = 79, so (83a + 76b)/(a + b) = 79. This gives 83a + 76b = 79a + 79b, so 4a = 3b, or a : b = 3 : 4. Similarly for B and C: (76b + 85c)/(b + c) = 81 gives 76b + 85c = 81b + 81c, so 4c = 5b, or c : b = 5 : 4. Taking a : b : c = 3 : 4 : 5, combined average = (83×3 + 76×4 + 85×5)/(3 + 4 + 5) = (249 + 304 + 425)/12 = 978/12 = 81.5.

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